# Construct truth tables to verify the following laws a ¬?...

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Mat1101 Tutorial Week 6 Logic Grossman Chapter 4 1. Construct truth tables to verify the following laws. (a) ¬(? ∨ ?) ≡ ¬? ∧ ¬? (de Morgan’s second law) ? ? ? ∨ ? ¬(? ∨ ?) ¬? ¬? ¬? ∧ ¬? T T T F F F F T F T F F T F F T T F T F F F F F T T T T (b) ? → ? ≡ ¬? ∨ ? (implication law) ? ? ? → ? ¬? ¬? ∨ ? T T T F T T F F F F F T T T T F F F T T (c) ? ∧ (? ∨ ?) ≡ ? (first absorption) ? ? ? ∨ ? ? ∧ (? ∨ ?) T T T T T F T T F T T F F F F F 2. Consider the following two propositions: ? ≡ It is snowing ? ≡ I go skiing . (a) Write the implication ? → ? in plain english.
(b) Write the inverse, the converse and the contrapositive of this implication using the logical symbols ∧, ∨, ¬, or as required.
(c) Construct truth tables of the implication, and it's inverse, converse, and contrapositive. Hence, determine which are logically equivalent.